Ultrafast modulation of electronic structure by coherent phonon excitations

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Ultrafast modulation of electronic structure by coherent phonon excitations

J. Weisshaupt, A. Rouzée, M. Woerner, M. J. J. Vrakking, T. Elsaesser, E. L. Shirley, and A. Borgschulte

Phys. Rev. B 95, 081101(R) – Published 1 February 2017

Abstract

Femtosecond x-ray absorption spectroscopy with a laser-driven high-harmonic source is used to map ultrafast changes of x-ray absorption by femtometer-scale coherent phonon displacements. In ${LiBH}_{4}$ , displacements along an $A_{g}$ phonon mode at 10 THz are induced by impulsive Raman excitation and give rise to oscillatory changes of x-ray absorption at the Li $K$ edge. Electron density maps from femtosecond x-ray diffraction data show that the electric field of the pump pulse induces a charge transfer from the ${BH}_{4}^{-}$ to neighboring ${Li}^{+}$ ions, resulting in a differential Coulomb force that drives lattice vibrations in this virtual transition state.

Received 24 October 2016

DOI:https://doi.org/10.1103/PhysRevB.95.081101

Physics Subject Headings (PhySH)

Insulators Phonons Stimulated Raman scattering

Polycrystalline materials

Density functional theory X-ray absorption spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

J. Weisshaupt¹, A. Rouzée¹, M. Woerner^1,*, M. J. J. Vrakking¹, T. Elsaesser¹, E. L. Shirley², and A. Borgschulte³

¹Max-Born-Institut für Nichtlineare Optik und Kurzzeitspektroskopie, D-12489 Berlin, Germany
²National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8441, USA
³Swiss Federal Laboratories for Materials Science and Technology, Laboratory for Advanced Analytical Technologies, EMPA, CH-8600 Dübendorf, Switzerland

^*woerner@mbi-berlin.de

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Issue

Vol. 95, Iss. 8 — 15 February 2017

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Images

Figure 1
(a) Unit cell of lithium borohydride with the ${Li}^{+}$ (green) and ${BH}_{4}^{-}$ ions (B: red; H: gray). The shaded area marks the $y = \frac{1}{4}$ plane. (b) Equilibrium electron density $ρ_{0} (r)$ in the $y = \frac{1}{4}$ plane. (c) Transient differential electronic charge density $Δ ρ (r, t = 0)$ reported in Ref. [24]. Red and blue coloration indicate negative and positive changes in the local electron density. The arrows indicate the impulsively excited 10 THz $A_{g}$ Raman mode. (d) Differential Coulomb potential $V_{diff} (r, 0)$ generated from the transient differential electron density in (c). The arrows indicate the electric field $\nabla V_{diff} (r, 0)$ . The boron nuclei are strongly accelerated by the impulsive force of the induced electronic polarization due to the strong overlap between the $A_{g}$ mode's elongations and the impulsive force.
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Figure 2
(a) Black: Linear absorption spectrum of ${LiBH}_{4}$ at the Li $K$ edge as measured with a two-color high-harmonic (HHG) source. Blue: Theoretical spectrum calculated using a Bethe-Salpeter approach. A transition into a bound excitonic state is observed at 60 eV, followed by transitions into free conduction band states at higher energies. The oscillations above 62 eV are due to band structure effects. A calculation without electron-hole interaction (green line) does not account for the experimental spectrum but does show the dipole-matrix-element-allowed density of states. Tick marks indicate the positions of high harmonics generated using an 800 nm laser used in transient absorption measurements shown in Figs. 3–3. (b) Theoretical x-ray absorption spectra calculated for strongly exaggerated elongation amplitudes of the 10 THz $A_{g}$ phonon mode in units of $[δ Q] = Å \sqrt{amu}$ . Pronounced absorption changes occur both in the excitonic and plateau regions of the spectral envelope.
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Figure 3
Transient change of x-ray absorption at (a) 61.5 eV and (b) 67.5 eV, the photon energies of individual harmonics. The change of absorption $Δ A = - ln (T / T_{0})$ is plotted as a function of pump-probe delay ( $T$ and $T_{0}$ are the sample transmission with and without excitation) with $1 σ$ error bars. Both transients display strong oscillations due to impulsively excited coherent phonons with a main frequency around 10 THz (solid lines). (c) Bottom: Fourier transform of the oscillations in (a). Top: Spontaneous Raman spectrum of ${LiBH}_{4}$ . (d) Transient absorption spectra measured with the two-color HHG source [symbols, note that the signal is higher than in (a) and (b) due to different experimental parameters] derived by averaging the absorption changes at the maxima and minima of oscillatory pump-probe traces. The solid lines are derived from the calculated spectra in Fig. 2 by rescaling the phonon elongations $δ Q$ to the values estimated from the experiments. The high optical density of the film sample did not allow for extending the measurements into the near-edge region of the spectrum, which features the excitonic peak.
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